# Ideal bandpass filter questions

I have this signal (as the text): $$x(t)=\sum_{k=-\infty}^\infty g(t-kT)\quad\text{with}\quad g(t)=\textrm{rect}(t)$$ then we have an ideal bandpass filter $H(f)$ with frequency centered at $f=20\textrm{ kHz}$ and band $b=10\textrm{ kHz}$. Calculate the signal's output in frequency and in time. This is a periodic signal. $$X(f)=\sum_{k=-\infty}^\infty C_n\delta(f-nf_0)$$ doubts:

$$C_n=f_0\mathrm{sinc}(nf_0)\quad\text{and output}\quad\sum_{k=-25}^{-15}{C_n\delta(f-nf_0)}+\sum_{k=15}^{25}{C_n\delta(f-nf_0)}\quad ?$$

• It's probably $g(t-kT)$ in the sum (and not $g(t-kt$)), and we have to know the value of $T$, otherwise the question can't be answered. – Matt L. Mar 29 '17 at 14:10
• have rect(t).So rect(t/T) with T=1 or mistake? – Santo1991 Mar 29 '17 at 14:16
• Done. missed T. T=0.1ms . thanks – Santo1991 Mar 29 '17 at 14:38